When position data from a global navigation satellite system is unavailable, a parameter, associated with a horizontal position (e.g. latitude and longitude) of a moveable object over a known surface such as terrain map, may be measured. Deterministic models may be used to determine the horizontal position.
A deterministic approach does not take into account model and sensor inaccuracies and noise. To address these shortcomings, non-linear Bayesian state estimators of stochastic dynamic systems may be used to estimate the horizontal position (and related parameters) of the moveable object on a known surface based upon a parameter associated with a horizontal position. However, a non-linear state estimator, based on a numerical solution of the Bayesian relations, i.e., a point mass filter, requires significant computation resources. The state estimator estimating three or more variables cannot be solved with typical data processing systems in a period of time consistent with application requirements. Therefore, there is a need to reduce the computational requirements for these non-linear estimators used to estimate the horizontal position (and related parameters) on a known surface based upon a measured parameter associated with the horizontal position.